Solving Design and Control Problems Involving Neural Network Surrogates
Dr. Sven Leyffer
, Argonne National Laboratory
In this talk, we consider nonlinear optimization problems that involve surrogate models represented by neural networks. We demonstrate how to directly embed neural network evaluation into optimization models, and highlight a difficulty with this approach that can prevent convergence. We then present two alternative formulations of these problems as mixed-integer optimization problems, and as optimization problems with complementarity constraints. Each of these formulations may be solved with state-of-the-art optimization methods, and we show how to obtain good initial feasible solutions for these methods. We compare our formulations on three practical applications arising in the design and control of combustion engines, in the generation of adversarial attacks on classifier networks, and in the determination of optimal flows in an oil well network.